Mini-Symposium

C. Advances on Boundary Element Methods

This mini-symposium will bring together researchers from academia and government laboratories, and engineers working in industry around the world to discuss the recent evolution of methods based on classical integral equations in Applied Mechanics. In particular, the Boundary Element Method (BEM), also known as the Boundary Integral Equation Method (BIEM), has become an established method of solution in several important areas of engineering such as fracture mechanics, acoustics, and solid dynamics, among others. The mini-symposium also aims to promote further international co-operation between scientists and engineers from different disciplines involved in the study and development of the Boundary Element Techniques.

Researchers from all countries are cordially invited to contribute with their recent work to this mini-symposium. Although the method has had an enormous growth in the last 30 years, there are still many areas where the method needs to be developed further. We are particularly searching for contributions covering new formulations and ideas for a wide range of applications as well as reports on advances made on the development and implementation of robust numerical tools that can be used to analyze complex problems in the context of Applied Mechanics and Engineering. Contributions on analysis of practical applications are very much encouraged.

Contributions addressing either the topics listed below or other topics of interest in Applied Mechanics and Engineering are appropriate for this mini-symposium.

Heat and mass transfer
Acoustics
Electrical engineering and electromagnetics
Fluid flow
Advanced formulations
Computational techniques
Software developments
Fast BEM formulations (multipole methods, wavelet methods, ACA, and others)
Advanced structural applications
Dynamics and vibrations
Damage mechanics and fracture
Composites, gradient materials, MEMS and others
Material characterisation
Financial Engineering Applications
Stochastic Modelling
Large-scale, multi-scale and multi-physics analysis
Biomedical, bioengineering applications
Emerging Applications

Symposium coordinators:

Prof. Euclides de Mesquita Neto, Ph.D.	Prof. Wilson Sergio Venturini, Ph.D.
Departamento de Mecânica Computacional	Departamento de Engenharia de Estruturas
FEM, UNICAMP	Escola de Engenharia de São Carlos
C. P. 6122	Universidade de São Paulo
Cidade Universitária	Av. Trabalhador Sãocarlense, 400
13081-970 - Campinas, SP , Brazil	13566-590 São Carlos, SP, Brazil
Phone: 55-19-35213203	Phone: 55-16-3373 9455
Fax: 55-19-35213722	Fax: 55-16-3373 9482
Prof. Ádrian P. Cisilino, Ph.D.	Prof. Leonard J. Gray, Ph.D.
Departamento de Ingeniería Mecánica Facultad de Ingeniería	Computer Science and Mathematics Division
Universidad Nacional de Mar del Plata	Oak Ridge National Laboratory
Av. Juan B. Justo 4302	P.O. Box 2008
Mar del Plata, Argentina	Oak Ridge, TN 37831, USA
Phone: +54 (223) 4816600 ext 186	Phone: +1 865 574 8189
Fax:   +54 (223) 4810046	Fax: +1 865 574 0680

 

INVITED LECTURE

LEVEL SET BOUNDARY INTEGRAL SIMULATIONS OF MOVING BOUNDARY PROBLEMS

LEONARD J. GRAY
Computer Science and Mathematics Division
Oak Ridge National Laboratory
Oak Ridge, TN 37831-6367, USA

 

ABSTRACT. Moving boundary problems have many important applications, and a boundary integral equation formulation is advantageous for their solution. Compared to working with the new volume, it is clearly an easier task to re-mesh the evolving boundary at every time step. Moreover, these simulations generally require knowledge of the surface gradient of the principal function, and these derivatives can be accurately obtained from the integral equations.

In this talk, recent work on the coupling of the integral equation formulation with the powerful level set method for tracking surface evolution is described. The two calculations to be discussed are the modeling of two-dimensional wave breaking over a sloping beach, and the pinch-off of an inviscid fluid column based upon a potential flow model with capillary forces (Raleigh-Taylor instability). In both cases the interface velocity is obtained from a linear element Galerkin boundary integral solution of the Laplace equation (2D and 3D axisymmetric, respectively); the algorithm for the critical post-processing evaluation of the surface potential gradient will be discussed. The free surface, together with its (potential) boundary values, are evolved using level set techniques on a fixed domain.

The Raleigh-Taylor simulations demonstrate that the algorithm is capable of handling topological change (pinch-off) and after pinch-off events. Near pinch-off, excellent agreement is obtained between the simulations and known scaling laws.

Acknowledgement. This research was supported by the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under contract DE-AC05-00OR22725 with UT-Battelle, LLC. Partial support from National Council for Scientific and Technological Development (CNPq) is also acknowledged.